Theorem exp42 300

Description: An exportation inference.

Hypothesis

Ref	Expression
exp42.1	⊢ (((φ ∧ (ψ ∧ χ)) ∧ θ) → τ)

Assertion

Ref	Expression
exp42	⊢ (φ → (ψ → (χ → (θ → τ))))

Proof of Theorem exp42

Step	Hyp	Ref	Expression
1		exp42.1	. . 3 ⊢ (((φ ∧ (ψ ∧ χ)) ∧ θ) → τ)
2	1	exp31 293	. 2 ⊢ (φ → ((ψ ∧ χ) → (θ → τ)))
3	2	exp3a 292	1 ⊢ (φ → (ψ → (χ → (θ → τ))))

Syntax hints:   → wi 2   ∧ wa 196

This theorem is referenced by:  isofrlem 2939  oelim 3137  en3d 3304  zornlem7 3609  infxpidmlem11 4943  shscl 5282  spanun 5450

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6

This theorem depends on definitions:  df-bi 128  df-an 198

metamath.org